173edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
173edo is the | 173edo is in[[consistent]] to the [[5-odd-limit]]. Two mappings are to be considered for the 5-limit: {{val| 173 274 402 }} ([[patent val]]) and {{val| 173 274 '''401''' }} (173c). | ||
[[ | Using the patent val, it [[tempering out|tempers out]] the [[unicorn comma]], 1594323/1562500 and the [[escapade comma]], 4294967296/4271484375 in the 5-limit; [[1728/1715]], [[3136/3125]], and 413343/409600 in the 7-limit; [[176/175]], [[540/539]], 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[semisept]] temperament; [[676/675]], [[847/845]], [[1188/1183]], and [[1287/1280]] in the 13-limit. | ||
[[ | |||
Using the 173e val, {{val| 173 271 402 486 '''599''' }}, it tempers out [[441/440]], 1944/1925, [[4000/3993]], and [[5632/5625]] in the 11-limit; [[364/363]], 676/675, [[1001/1000]], and 3159/3125 in the 13-limit. Using the 173ef val, {{val| 173 271 402 486 '''599 641''' }}, [[144/143]], 351/350, [[640/637]], and 847/845 are tempered out in the 13-limit. | |||
Using the 173d val, {{val| 173 271 402 '''485''' }}, it tempers out [[126/125]], [[10976/10935]], and 28824005/28311552 in the 7-limit; [[385/384]], 1617/1600, 12005/11979, and [[14641/14580]] in the 11-limit; [[196/195]], [[351/350]], 676/675, 1287/1280, and [[10648/10647]] in the 13-limit, supporting the [[Unicorn family #Camahueto|camahueto]] temperament. | |||
Using the 173c val, it tempers out the [[amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; [[2430/2401]], [[4000/3969]], and 234375/229376 in the 7-limit, supporting the 7-limit [[hamity]] temperament. Using the alternative 173cd val, {{val| 173 271 '''401 485''' }} it tempers out [[225/224]], 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[septimin]] temperament; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; [[325/324]], [[729/728]], 847/845, and 1875/1859 in the 13-limit. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|173}} | |||
=== Subsets and supersets === | |||
173edo is the 40th [[prime edo]]. | |||
Latest revision as of 16:37, 20 February 2025
| ← 172edo | 173edo | 174edo → |
173 equal divisions of the octave (abbreviated 173edo or 173ed2), also called 173-tone equal temperament (173tet) or 173 equal temperament (173et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 173 equal parts of about 6.94 ¢ each. Each step represents a frequency ratio of 21/173, or the 173rd root of 2.
173edo is inconsistent to the 5-odd-limit. Two mappings are to be considered for the 5-limit: ⟨173 274 402] (patent val) and ⟨173 274 401] (173c).
Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the escapade comma, 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit semisept temperament; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit.
Using the 173e val, ⟨173 271 402 486 599], it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, ⟨173 271 402 486 599 641], 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.
Using the 173d val, ⟨173 271 402 485], it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the camahueto temperament.
Using the 173c val, it tempers out the amity comma, 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit hamity temperament. Using the alternative 173cd val, ⟨173 271 401 485] it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit septimin temperament; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.38 | +2.13 | +2.27 | -3.34 | -1.22 | -0.91 | +0.75 | +2.94 | -2.99 | -0.53 |
| Relative (%) | +0.0 | -19.9 | +30.6 | +32.8 | -48.2 | -17.6 | -13.1 | +10.9 | +42.4 | -43.1 | -7.6 | |
| Steps (reduced) |
173 (0) |
274 (101) |
402 (56) |
486 (140) |
598 (79) |
640 (121) |
707 (15) |
735 (43) |
783 (91) |
840 (148) |
857 (165) | |
Subsets and supersets
173edo is the 40th prime edo.